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On finite simply reducible groups
Author(s):
L.
S.
Kazarin;
V.
V.
Yanishevskiĭ
Translated by:
B. M. Bekker
Original publication:
Algebra i Analiz,
tom 19
(2007),
nomer 6.
Journal:
St. Petersburg Math. J.
19
(2008),
931-951.
MSC (2000):
Primary 53A04;
Secondary 52A40., 52A10
Posted:
August 21, 2008
MathSciNet review:
2411640
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References |
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Abstract:
A finite group  is said to be simply reducible ( -group) if it has the following two properties: 1) each element of  is conjugate to its inverse; 2) the tensor product of every two irreducible representations is decomposed as a sum of irreducible representations of  with multiplicities not exceeding 1. It is proved that a finite  -group is solvable if it has no composition factors isomorphic to the alternating groups  or  .
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Additional Information:
L.
S.
Kazarin
Affiliation:
Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
Email:
kazarin@uniyar.ac.ru
V.
V.
Yanishevskiĭ
Affiliation:
Mathematics Department, Yaroslavl Demidov State University, Sovetskaya 14, Yaroslavl 150000, Russia
Email:
yvitaliy@rambler.ru
DOI:
10.1090/S1061-0022-08-01028-5
PII:
S 1061-0022(08)01028-5
Keywords:
Group,
subgroup,
irreducible representation,
character,
tensor product,
real element
Received by editor(s):
14/FEB/2007
Posted:
August 21, 2008
Additional Notes:
The first author was supported by RFBR (grant no.~05-01-01018)
Dedicated:
Dedicated to the centenary of D. K. Faddeev's birth
Copyright of article:
Copyright
2008,
American Mathematical Society
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